Igor A. Litvin

A digital laser for on-demand laser modes

Customizing the output beam shape from a laser invariably involves specialized optical elements in the form of apertures, diffractive optics and free-form mirrors. Such optics require considerable design and fabrication effort and suffer from the further disadvantage of being immutably connected to the selection of a particular spatial mode. Here we overcome these limitations with the first digital laser comprising an electrically addressed reflective phase-only spatial light modulator as an intra-cavity digitally addressed holographic mirror. The phase and amplitude of the holographic mirror may be controlled simply by writing a computer-generated hologram in the form of a grey-scale image to the device, for on-demand laser modes. We show that we can digitally control the laser modes with ease, and demonstrate real-time switching between spatial modes in an otherwise standard solid-state laser resonator. Our work opens new possibilities for the customizing of laser modes at source.

Azimuthal decomposition with digital holograms

We demonstrate a simple approach, using digital holograms, to perform a complete azimuthal decomposition of an optical field. Importantly, we use a set of basis functions that are not scale dependent so that unlike other methods, no knowledge of the initial field is required for the decomposition. We illustrate the power of the method by decomposing two examples: superpositions of Bessel beams and Hermite-Gaussian beams (off-axis vortex). From the measured decomposition we show reconstruction of the amplitude, phase and orbital angular momentum density of the field with a high degree of accuracy.

Poynting vector and orbital angular momentum density of superpositions of Bessel beams

We study theoretically the orbital angular momentum (OAM) density in arbitrary scalar optical fields, and outline a simple approach using only a spatial light modulator to measure this density. We demonstrate the theory in the laboratory by creating superpositions of non-diffracting Bessel beams with digital holograms, and find that the OAM distribution in the superposition field matches the predicted values. Knowledge of the OAM distribution has relevance in optical trapping and tweezing, and quantum information processing.

Quantitative measurement of the orbital angular momentum density of light

In this work we derive expressions for the orbital angular momentum (OAM) density of light, for both symmetric and nonsymmetric optical fields, that allow a direct comparison between theory and experiment. We present a simple method for measuring the OAM density in optical fields and test the approach on superimposed nondiffracting higher-order Bessel beams. The measurement technique makes use of a single spatial light modulator and a Fourier transforming lens to measure the OAM spectrum of the optical field. Quantitative values for the OAM density as a function of the radial position in the optical field are obtained for both symmetric and nonsymmetric superpositions, illustrating good agreement with the theoretical prediction.

Gaussian mode selection with intracavity diffractive optics

We outline a resonator design that allows for the selection of a Gaussian mode by diffractive optical elements. This is made possible by the metamorphosis of a Gaussian beam into a flat-top beam during propagation from one end of the resonator to the other. By placing the gain medium at the flat-top beam end, it is possible to extract high energy in a low-loss cavity. A further feature of this resonator is the ability to select the field properties at either end of the cavity almost independently, thus opening the way to minimize the output divergence while simultaneously maximizing the output energy.

Doughnut laser beam as an incoherent superposition of two petal beams

Laguerre-Gaussian beams with a nonzero azimuthal index are known to carry orbital angular momentum (OAM), and are routinely created external to laser cavities. The few reports of obtaining such beams from laser cavities suffer from inconclusive evidence of the real electromagnetic field. In this Letter we revisit this question and show that an observed doughnut beam from a laser cavity may not be a pure Laguerre-Gaussian azimuthal mode but can be an incoherent sum of petal modes, which do not carry OAM. We point out the requirements for future analysis of such fields from laser resonators.

Petal-like modes in Porro prism resonators

A new approach to modeling the spatial intensity profile from Porro prism resonators is proposed based on rotating loss screens to mimic the apex losses of the prisms. A numerical model based on this approach is presented which correctly predicts the output transverse field distribution found experimentally from such resonators.

Generation and propagation dynamics of obstructed and unobstructed rotating orbital angular momentum-carrying Helicon beams

We report on the dynamics of propagation of rotating OAM-carrying beams past partial and total obstructions. We demonstrate a simple experimental technique for generating rotating Helicon beams and for investigating the propagation of the obstructed field. In this technique we create digital holograms, imprinted on a spatial light modulator, that simultaneously vary the amplitude and phase of the light to create a digital equivalent of multiple ring slit apertures. Our method allows for the controlled generation of Helicon beams of any order, and any radial wavevector, thus controlling the rotation rate of the beams. We further study the reconstruction properties for total on-axis obstructions as compared to partial off-axis obstructions and show that the results obtained are in good agreement with theoretical predictions.

Tuneable Gaussian to flat-top resonator by amplitude beam shaping

We outline a simple laser cavity comprising an opaque ring and a circular aperture that is capable of producing spatially tuneable laser modes, from a Gaussian beam to a Flat-top beam. The tuneability is achieved by varying the diameter of the aperture and thus requires no realignment of the cavity. We demonstrate this principle using a digital laser with an intra-cavity spatial light modulator, and confirm the predicted properties of the resonator experimentally.

Angular self-reconstruction of petal-like beams.

The self-reconstruction of superpositions of Laguerre-Gaussian (LG) beams has been observed experimentally, but the results appear anomalous and without a means to predict under what conditions this take place. In this Letter, we offer a simple equation for predicting the self-reconstruction distance of superpositions of LG beams, which we confirm by numerical propagation as well as by experiment. We explain that the self-reconstruction process is not guaranteed and predict its dependence on the obstacle location and obstacle size.